Abstract

Ion beam figuring technology for low-gradient mirrors is discussed. Ion beam figuring is a noncontact machining technique in which a beam of high-energy ions is directed toward a target workpiece to remove material in a predetermined and controlled fashion. Owing to this noncontact mode of material removal, problems associated with tool wear and edge effects, which are common in conventional contact polishing processes, are avoided. Based on the Bayesian principle, an iterative dwell time algorithm for planar mirrors is deduced from the computer-controlled optical surfacing (CCOS) principle. With the properties of the removal function, the shaping process of low-gradient mirrors can be approximated by the linear model for planar mirrors. With these discussions, the error surface figuring technology for low-gradient mirrors with a linear path is set up. With the near-Gaussian property of the removal function, the figuring process with a spiral path can be described by the conventional linear CCOS principle, and a Bayesian-based iterative algorithm can be used to deconvolute the dwell time. Moreover, the selection criterion of the spiral parameter is given. Ion beam figuring technology with a spiral scan path based on these methods can be used to figure mirrors with non-axis-symmetrical errors. Experiments on SiC chemical vapor deposition planar and Zerodur paraboloid samples are made, and the final surface errors are all below 1/100λ.

© 2009 Optical Society of America

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References

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  1. S. R. Wilson, D. W. Reicher, and J. R. McNeil, “Surface figuring using neutral ion beams,” Proc. SPIE 966, 74-81 (1988).
  2. R. Klaver, “Novel interferometer to measure the figure of strongly aspherical mirrors,” master's thesis (The Netherlands University of Delft, 2001).
  3. K. W. Hylton, C. L. Carnal, J. R. Jackson, and C. M. Egert, “Ion beam milling of silicon carbide optical components,” Proc. SPIE 1994, 16-26 (1994).
    [CrossRef]
  4. L. N. Allen, J. J. Hannon, and R. M. Wambach, “Final surface error correction of an off-axis aspheric petal by ion figuring,” Proc. SPIE 1543, 190-200 (1992).
    [CrossRef]
  5. S. R. Wilson and J. R. Mcneil, “Neutral ion beam figuring of large optical surfaces,” Proc. SPIE 818, 320-324 (1987).
  6. L. N. Allen and R. E. Keim. “An ion figuring system for large optic fabrication,” Proc. SPIE 1168, 33-50 (1989).
  7. L. N. Allen, R. E. Keim, and T. S. Lewis. “Surface error correction of a Keck 10 -m telescope primary segment by ion figuring,” Proc. SPIE 1531, 195-204 (1991).
    [CrossRef]
  8. C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54-62 (1992).
    [CrossRef]
  9. C. J. Jiao, S. Y. Li, X. H. Xie, D. F. Wang, and L. Zhou, “Controllability of removal function in the ion beam figuring process for optics mirrors,” Opt. Technique 34, 651-654(2008), in Chinese.
  10. L. Yang, Advanced Technology of Optics Manufacturing (Science Press, 2001).
  11. R. Molina, J. Nunez, F. Cortijo, and J. Mateos, “Image restoration in astronomy: a Bayesian perspective,” IEEE Signal Process. Lett. 18, 11-29 (2001).
    [CrossRef]
  12. C. Z. Fang, and D. Y. Xiao, Process Identification (Tsinghua Univ. Press, 1998).
  13. D. Nicolas, B. F. Laure, Z. Christophe, R. Pascal, K. Zvi, O. M. Jean Christophe, and Z. Josiane, “3D microscopy deconvolution using Richardon-Lucy algorithm with total variation regularization,” http://hal.inria.fr/inria-00070726/en.
  14. L. B. Lucy, “An iterative technique for the rectification of observed distribution,” Astron. J. 79, 745-754 (1974).
    [CrossRef]
  15. W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62, 55-59 (1972).
    [CrossRef]
  16. D. C. Dobson and C. R. Vogel, “Convergence of an iterative method for total variation denoising,” SIAM J. Numer. Anal. 34, 1779-1791 (1997).
    [CrossRef]
  17. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D (Amsterdam) 60, 259-268 (1992).
    [CrossRef]
  18. L. Hocheol and Y. Minyang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt.Eng. 40, 1936-1943 (2001).
    [CrossRef]
  19. X. Q. Peng, Y. F. Dai, S. Y. Li, and W. W. You, “Dwell time algorithm for MRF of axis-symmetrical aspherical parts,” J. National University Defense Technol. 26 (3), 89-92(2004).
  20. A. Schindler, G. Boehm, T. Haensel, W. Frank, A. Nickel, B. Rauschenbach, and F. Bigl, “Precision optical asphere fabrication by plasma jet chemical etching (PJCE) and ion beam figuring,” Proc. SPIE 4451, 242-248 (2001).
    [CrossRef]
  21. S. C. Fawcett, T. W. Drueding, and T. G. Bifano, “Neutral ion figuring of chemical vapor deposited SiC,” Opt. Eng. 33, 967-974 (1994).
    [CrossRef]
  22. T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Deconvolution algorithm applied to ion figuring,” Vol. 13 of OSA Technical Digest Series (Optical Society of America, 1994), pp. 244-247.

2008 (1)

C. J. Jiao, S. Y. Li, X. H. Xie, D. F. Wang, and L. Zhou, “Controllability of removal function in the ion beam figuring process for optics mirrors,” Opt. Technique 34, 651-654(2008), in Chinese.

2004 (1)

X. Q. Peng, Y. F. Dai, S. Y. Li, and W. W. You, “Dwell time algorithm for MRF of axis-symmetrical aspherical parts,” J. National University Defense Technol. 26 (3), 89-92(2004).

2001 (3)

A. Schindler, G. Boehm, T. Haensel, W. Frank, A. Nickel, B. Rauschenbach, and F. Bigl, “Precision optical asphere fabrication by plasma jet chemical etching (PJCE) and ion beam figuring,” Proc. SPIE 4451, 242-248 (2001).
[CrossRef]

L. Hocheol and Y. Minyang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt.Eng. 40, 1936-1943 (2001).
[CrossRef]

R. Molina, J. Nunez, F. Cortijo, and J. Mateos, “Image restoration in astronomy: a Bayesian perspective,” IEEE Signal Process. Lett. 18, 11-29 (2001).
[CrossRef]

1997 (1)

D. C. Dobson and C. R. Vogel, “Convergence of an iterative method for total variation denoising,” SIAM J. Numer. Anal. 34, 1779-1791 (1997).
[CrossRef]

1994 (2)

S. C. Fawcett, T. W. Drueding, and T. G. Bifano, “Neutral ion figuring of chemical vapor deposited SiC,” Opt. Eng. 33, 967-974 (1994).
[CrossRef]

K. W. Hylton, C. L. Carnal, J. R. Jackson, and C. M. Egert, “Ion beam milling of silicon carbide optical components,” Proc. SPIE 1994, 16-26 (1994).
[CrossRef]

1992 (3)

L. N. Allen, J. J. Hannon, and R. M. Wambach, “Final surface error correction of an off-axis aspheric petal by ion figuring,” Proc. SPIE 1543, 190-200 (1992).
[CrossRef]

C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54-62 (1992).
[CrossRef]

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D (Amsterdam) 60, 259-268 (1992).
[CrossRef]

1991 (1)

L. N. Allen, R. E. Keim, and T. S. Lewis. “Surface error correction of a Keck 10 -m telescope primary segment by ion figuring,” Proc. SPIE 1531, 195-204 (1991).
[CrossRef]

1989 (1)

L. N. Allen and R. E. Keim. “An ion figuring system for large optic fabrication,” Proc. SPIE 1168, 33-50 (1989).

1988 (1)

S. R. Wilson, D. W. Reicher, and J. R. McNeil, “Surface figuring using neutral ion beams,” Proc. SPIE 966, 74-81 (1988).

1987 (1)

S. R. Wilson and J. R. Mcneil, “Neutral ion beam figuring of large optical surfaces,” Proc. SPIE 818, 320-324 (1987).

1974 (1)

L. B. Lucy, “An iterative technique for the rectification of observed distribution,” Astron. J. 79, 745-754 (1974).
[CrossRef]

1972 (1)

Allen, L. N.

L. N. Allen, J. J. Hannon, and R. M. Wambach, “Final surface error correction of an off-axis aspheric petal by ion figuring,” Proc. SPIE 1543, 190-200 (1992).
[CrossRef]

L. N. Allen, R. E. Keim, and T. S. Lewis. “Surface error correction of a Keck 10 -m telescope primary segment by ion figuring,” Proc. SPIE 1531, 195-204 (1991).
[CrossRef]

L. N. Allen and R. E. Keim. “An ion figuring system for large optic fabrication,” Proc. SPIE 1168, 33-50 (1989).

Bifano, T. G.

S. C. Fawcett, T. W. Drueding, and T. G. Bifano, “Neutral ion figuring of chemical vapor deposited SiC,” Opt. Eng. 33, 967-974 (1994).
[CrossRef]

T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Deconvolution algorithm applied to ion figuring,” Vol. 13 of OSA Technical Digest Series (Optical Society of America, 1994), pp. 244-247.

Bigl, F.

A. Schindler, G. Boehm, T. Haensel, W. Frank, A. Nickel, B. Rauschenbach, and F. Bigl, “Precision optical asphere fabrication by plasma jet chemical etching (PJCE) and ion beam figuring,” Proc. SPIE 4451, 242-248 (2001).
[CrossRef]

Boehm, G.

A. Schindler, G. Boehm, T. Haensel, W. Frank, A. Nickel, B. Rauschenbach, and F. Bigl, “Precision optical asphere fabrication by plasma jet chemical etching (PJCE) and ion beam figuring,” Proc. SPIE 4451, 242-248 (2001).
[CrossRef]

Carnal, C. L.

K. W. Hylton, C. L. Carnal, J. R. Jackson, and C. M. Egert, “Ion beam milling of silicon carbide optical components,” Proc. SPIE 1994, 16-26 (1994).
[CrossRef]

C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54-62 (1992).
[CrossRef]

Christophe, Z.

D. Nicolas, B. F. Laure, Z. Christophe, R. Pascal, K. Zvi, O. M. Jean Christophe, and Z. Josiane, “3D microscopy deconvolution using Richardon-Lucy algorithm with total variation regularization,” http://hal.inria.fr/inria-00070726/en.

Cortijo, F.

R. Molina, J. Nunez, F. Cortijo, and J. Mateos, “Image restoration in astronomy: a Bayesian perspective,” IEEE Signal Process. Lett. 18, 11-29 (2001).
[CrossRef]

Dai, Y. F.

X. Q. Peng, Y. F. Dai, S. Y. Li, and W. W. You, “Dwell time algorithm for MRF of axis-symmetrical aspherical parts,” J. National University Defense Technol. 26 (3), 89-92(2004).

Dobson, D. C.

D. C. Dobson and C. R. Vogel, “Convergence of an iterative method for total variation denoising,” SIAM J. Numer. Anal. 34, 1779-1791 (1997).
[CrossRef]

Drueding, T. W.

S. C. Fawcett, T. W. Drueding, and T. G. Bifano, “Neutral ion figuring of chemical vapor deposited SiC,” Opt. Eng. 33, 967-974 (1994).
[CrossRef]

T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Deconvolution algorithm applied to ion figuring,” Vol. 13 of OSA Technical Digest Series (Optical Society of America, 1994), pp. 244-247.

Egert, C. M.

K. W. Hylton, C. L. Carnal, J. R. Jackson, and C. M. Egert, “Ion beam milling of silicon carbide optical components,” Proc. SPIE 1994, 16-26 (1994).
[CrossRef]

C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54-62 (1992).
[CrossRef]

Fang, C. Z.

C. Z. Fang, and D. Y. Xiao, Process Identification (Tsinghua Univ. Press, 1998).

Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D (Amsterdam) 60, 259-268 (1992).
[CrossRef]

Fawcett, S. C.

S. C. Fawcett, T. W. Drueding, and T. G. Bifano, “Neutral ion figuring of chemical vapor deposited SiC,” Opt. Eng. 33, 967-974 (1994).
[CrossRef]

T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Deconvolution algorithm applied to ion figuring,” Vol. 13 of OSA Technical Digest Series (Optical Society of America, 1994), pp. 244-247.

Frank, W.

A. Schindler, G. Boehm, T. Haensel, W. Frank, A. Nickel, B. Rauschenbach, and F. Bigl, “Precision optical asphere fabrication by plasma jet chemical etching (PJCE) and ion beam figuring,” Proc. SPIE 4451, 242-248 (2001).
[CrossRef]

Haensel, T.

A. Schindler, G. Boehm, T. Haensel, W. Frank, A. Nickel, B. Rauschenbach, and F. Bigl, “Precision optical asphere fabrication by plasma jet chemical etching (PJCE) and ion beam figuring,” Proc. SPIE 4451, 242-248 (2001).
[CrossRef]

Hannon, J. J.

L. N. Allen, J. J. Hannon, and R. M. Wambach, “Final surface error correction of an off-axis aspheric petal by ion figuring,” Proc. SPIE 1543, 190-200 (1992).
[CrossRef]

Hocheol, L.

L. Hocheol and Y. Minyang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt.Eng. 40, 1936-1943 (2001).
[CrossRef]

Hylton, K. W.

K. W. Hylton, C. L. Carnal, J. R. Jackson, and C. M. Egert, “Ion beam milling of silicon carbide optical components,” Proc. SPIE 1994, 16-26 (1994).
[CrossRef]

C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54-62 (1992).
[CrossRef]

Jackson, J. R.

K. W. Hylton, C. L. Carnal, J. R. Jackson, and C. M. Egert, “Ion beam milling of silicon carbide optical components,” Proc. SPIE 1994, 16-26 (1994).
[CrossRef]

Jean Christophe, O. M.

D. Nicolas, B. F. Laure, Z. Christophe, R. Pascal, K. Zvi, O. M. Jean Christophe, and Z. Josiane, “3D microscopy deconvolution using Richardon-Lucy algorithm with total variation regularization,” http://hal.inria.fr/inria-00070726/en.

Jiao, C. J.

C. J. Jiao, S. Y. Li, X. H. Xie, D. F. Wang, and L. Zhou, “Controllability of removal function in the ion beam figuring process for optics mirrors,” Opt. Technique 34, 651-654(2008), in Chinese.

Josiane, Z.

D. Nicolas, B. F. Laure, Z. Christophe, R. Pascal, K. Zvi, O. M. Jean Christophe, and Z. Josiane, “3D microscopy deconvolution using Richardon-Lucy algorithm with total variation regularization,” http://hal.inria.fr/inria-00070726/en.

Keim, R. E.

L. N. Allen, R. E. Keim, and T. S. Lewis. “Surface error correction of a Keck 10 -m telescope primary segment by ion figuring,” Proc. SPIE 1531, 195-204 (1991).
[CrossRef]

L. N. Allen and R. E. Keim. “An ion figuring system for large optic fabrication,” Proc. SPIE 1168, 33-50 (1989).

Klaver, R.

R. Klaver, “Novel interferometer to measure the figure of strongly aspherical mirrors,” master's thesis (The Netherlands University of Delft, 2001).

Laure, B. F.

D. Nicolas, B. F. Laure, Z. Christophe, R. Pascal, K. Zvi, O. M. Jean Christophe, and Z. Josiane, “3D microscopy deconvolution using Richardon-Lucy algorithm with total variation regularization,” http://hal.inria.fr/inria-00070726/en.

Lewis, T. S.

L. N. Allen, R. E. Keim, and T. S. Lewis. “Surface error correction of a Keck 10 -m telescope primary segment by ion figuring,” Proc. SPIE 1531, 195-204 (1991).
[CrossRef]

Li, S. Y.

C. J. Jiao, S. Y. Li, X. H. Xie, D. F. Wang, and L. Zhou, “Controllability of removal function in the ion beam figuring process for optics mirrors,” Opt. Technique 34, 651-654(2008), in Chinese.

X. Q. Peng, Y. F. Dai, S. Y. Li, and W. W. You, “Dwell time algorithm for MRF of axis-symmetrical aspherical parts,” J. National University Defense Technol. 26 (3), 89-92(2004).

Lucy, L. B.

L. B. Lucy, “An iterative technique for the rectification of observed distribution,” Astron. J. 79, 745-754 (1974).
[CrossRef]

Mateos, J.

R. Molina, J. Nunez, F. Cortijo, and J. Mateos, “Image restoration in astronomy: a Bayesian perspective,” IEEE Signal Process. Lett. 18, 11-29 (2001).
[CrossRef]

McNeil, J. R.

S. R. Wilson, D. W. Reicher, and J. R. McNeil, “Surface figuring using neutral ion beams,” Proc. SPIE 966, 74-81 (1988).

S. R. Wilson and J. R. Mcneil, “Neutral ion beam figuring of large optical surfaces,” Proc. SPIE 818, 320-324 (1987).

Minyang, Y.

L. Hocheol and Y. Minyang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt.Eng. 40, 1936-1943 (2001).
[CrossRef]

Molina, R.

R. Molina, J. Nunez, F. Cortijo, and J. Mateos, “Image restoration in astronomy: a Bayesian perspective,” IEEE Signal Process. Lett. 18, 11-29 (2001).
[CrossRef]

Nickel, A.

A. Schindler, G. Boehm, T. Haensel, W. Frank, A. Nickel, B. Rauschenbach, and F. Bigl, “Precision optical asphere fabrication by plasma jet chemical etching (PJCE) and ion beam figuring,” Proc. SPIE 4451, 242-248 (2001).
[CrossRef]

Nicolas, D.

D. Nicolas, B. F. Laure, Z. Christophe, R. Pascal, K. Zvi, O. M. Jean Christophe, and Z. Josiane, “3D microscopy deconvolution using Richardon-Lucy algorithm with total variation regularization,” http://hal.inria.fr/inria-00070726/en.

Nunez, J.

R. Molina, J. Nunez, F. Cortijo, and J. Mateos, “Image restoration in astronomy: a Bayesian perspective,” IEEE Signal Process. Lett. 18, 11-29 (2001).
[CrossRef]

Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D (Amsterdam) 60, 259-268 (1992).
[CrossRef]

Pascal, R.

D. Nicolas, B. F. Laure, Z. Christophe, R. Pascal, K. Zvi, O. M. Jean Christophe, and Z. Josiane, “3D microscopy deconvolution using Richardon-Lucy algorithm with total variation regularization,” http://hal.inria.fr/inria-00070726/en.

Peng, X. Q.

X. Q. Peng, Y. F. Dai, S. Y. Li, and W. W. You, “Dwell time algorithm for MRF of axis-symmetrical aspherical parts,” J. National University Defense Technol. 26 (3), 89-92(2004).

Rauschenbach, B.

A. Schindler, G. Boehm, T. Haensel, W. Frank, A. Nickel, B. Rauschenbach, and F. Bigl, “Precision optical asphere fabrication by plasma jet chemical etching (PJCE) and ion beam figuring,” Proc. SPIE 4451, 242-248 (2001).
[CrossRef]

Reicher, D. W.

S. R. Wilson, D. W. Reicher, and J. R. McNeil, “Surface figuring using neutral ion beams,” Proc. SPIE 966, 74-81 (1988).

Richardson, W. H.

Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D (Amsterdam) 60, 259-268 (1992).
[CrossRef]

Schindler, A.

A. Schindler, G. Boehm, T. Haensel, W. Frank, A. Nickel, B. Rauschenbach, and F. Bigl, “Precision optical asphere fabrication by plasma jet chemical etching (PJCE) and ion beam figuring,” Proc. SPIE 4451, 242-248 (2001).
[CrossRef]

Vogel, C. R.

D. C. Dobson and C. R. Vogel, “Convergence of an iterative method for total variation denoising,” SIAM J. Numer. Anal. 34, 1779-1791 (1997).
[CrossRef]

Wambach, R. M.

L. N. Allen, J. J. Hannon, and R. M. Wambach, “Final surface error correction of an off-axis aspheric petal by ion figuring,” Proc. SPIE 1543, 190-200 (1992).
[CrossRef]

Wang, D. F.

C. J. Jiao, S. Y. Li, X. H. Xie, D. F. Wang, and L. Zhou, “Controllability of removal function in the ion beam figuring process for optics mirrors,” Opt. Technique 34, 651-654(2008), in Chinese.

Wilson, S. R.

S. R. Wilson, D. W. Reicher, and J. R. McNeil, “Surface figuring using neutral ion beams,” Proc. SPIE 966, 74-81 (1988).

S. R. Wilson and J. R. Mcneil, “Neutral ion beam figuring of large optical surfaces,” Proc. SPIE 818, 320-324 (1987).

Xiao, D. Y.

C. Z. Fang, and D. Y. Xiao, Process Identification (Tsinghua Univ. Press, 1998).

Xie, X. H.

C. J. Jiao, S. Y. Li, X. H. Xie, D. F. Wang, and L. Zhou, “Controllability of removal function in the ion beam figuring process for optics mirrors,” Opt. Technique 34, 651-654(2008), in Chinese.

Yang, L.

L. Yang, Advanced Technology of Optics Manufacturing (Science Press, 2001).

You, W. W.

X. Q. Peng, Y. F. Dai, S. Y. Li, and W. W. You, “Dwell time algorithm for MRF of axis-symmetrical aspherical parts,” J. National University Defense Technol. 26 (3), 89-92(2004).

Zhou, L.

C. J. Jiao, S. Y. Li, X. H. Xie, D. F. Wang, and L. Zhou, “Controllability of removal function in the ion beam figuring process for optics mirrors,” Opt. Technique 34, 651-654(2008), in Chinese.

Zvi, K.

D. Nicolas, B. F. Laure, Z. Christophe, R. Pascal, K. Zvi, O. M. Jean Christophe, and Z. Josiane, “3D microscopy deconvolution using Richardon-Lucy algorithm with total variation regularization,” http://hal.inria.fr/inria-00070726/en.

Astron. J. (1)

L. B. Lucy, “An iterative technique for the rectification of observed distribution,” Astron. J. 79, 745-754 (1974).
[CrossRef]

IEEE Signal Process. Lett. (1)

R. Molina, J. Nunez, F. Cortijo, and J. Mateos, “Image restoration in astronomy: a Bayesian perspective,” IEEE Signal Process. Lett. 18, 11-29 (2001).
[CrossRef]

J. National University Defense Technol. (1)

X. Q. Peng, Y. F. Dai, S. Y. Li, and W. W. You, “Dwell time algorithm for MRF of axis-symmetrical aspherical parts,” J. National University Defense Technol. 26 (3), 89-92(2004).

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

S. C. Fawcett, T. W. Drueding, and T. G. Bifano, “Neutral ion figuring of chemical vapor deposited SiC,” Opt. Eng. 33, 967-974 (1994).
[CrossRef]

Opt. Technique (1)

C. J. Jiao, S. Y. Li, X. H. Xie, D. F. Wang, and L. Zhou, “Controllability of removal function in the ion beam figuring process for optics mirrors,” Opt. Technique 34, 651-654(2008), in Chinese.

Opt.Eng. (1)

L. Hocheol and Y. Minyang, “Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold,” Opt.Eng. 40, 1936-1943 (2001).
[CrossRef]

Physica D (Amsterdam) (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D (Amsterdam) 60, 259-268 (1992).
[CrossRef]

Proc. SPIE (8)

A. Schindler, G. Boehm, T. Haensel, W. Frank, A. Nickel, B. Rauschenbach, and F. Bigl, “Precision optical asphere fabrication by plasma jet chemical etching (PJCE) and ion beam figuring,” Proc. SPIE 4451, 242-248 (2001).
[CrossRef]

S. R. Wilson, D. W. Reicher, and J. R. McNeil, “Surface figuring using neutral ion beams,” Proc. SPIE 966, 74-81 (1988).

K. W. Hylton, C. L. Carnal, J. R. Jackson, and C. M. Egert, “Ion beam milling of silicon carbide optical components,” Proc. SPIE 1994, 16-26 (1994).
[CrossRef]

L. N. Allen, J. J. Hannon, and R. M. Wambach, “Final surface error correction of an off-axis aspheric petal by ion figuring,” Proc. SPIE 1543, 190-200 (1992).
[CrossRef]

S. R. Wilson and J. R. Mcneil, “Neutral ion beam figuring of large optical surfaces,” Proc. SPIE 818, 320-324 (1987).

L. N. Allen and R. E. Keim. “An ion figuring system for large optic fabrication,” Proc. SPIE 1168, 33-50 (1989).

L. N. Allen, R. E. Keim, and T. S. Lewis. “Surface error correction of a Keck 10 -m telescope primary segment by ion figuring,” Proc. SPIE 1531, 195-204 (1991).
[CrossRef]

C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion beam milling of optical components,” Proc. SPIE 1752, 54-62 (1992).
[CrossRef]

SIAM J. Numer. Anal. (1)

D. C. Dobson and C. R. Vogel, “Convergence of an iterative method for total variation denoising,” SIAM J. Numer. Anal. 34, 1779-1791 (1997).
[CrossRef]

Other (5)

C. Z. Fang, and D. Y. Xiao, Process Identification (Tsinghua Univ. Press, 1998).

D. Nicolas, B. F. Laure, Z. Christophe, R. Pascal, K. Zvi, O. M. Jean Christophe, and Z. Josiane, “3D microscopy deconvolution using Richardon-Lucy algorithm with total variation regularization,” http://hal.inria.fr/inria-00070726/en.

R. Klaver, “Novel interferometer to measure the figure of strongly aspherical mirrors,” master's thesis (The Netherlands University of Delft, 2001).

L. Yang, Advanced Technology of Optics Manufacturing (Science Press, 2001).

T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Deconvolution algorithm applied to ion figuring,” Vol. 13 of OSA Technical Digest Series (Optical Society of America, 1994), pp. 244-247.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram for edge extension with the Gaussian method.

Fig. 2
Fig. 2

Diagram for analysis of realization error with approximated velocity.

Fig. 3
Fig. 3

Schematic diagram for ion beam figuring with a spiral path.

Fig. 4
Fig. 4

Figuring result on CVD SiC with a linear scan path.

Fig. 5
Fig. 5

Figuring result on parabolic sample with a linear scan path.

Fig. 6
Fig. 6

Figuring result on parabolic sample with a spiral scan path.

Fig. 7
Fig. 7

Schematic drawing of the spiral path in a figuring experiment.

Equations (25)

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E ( x , y ) = Ω R ( x x , y y ) T ( x , y ) d x d y = R T .
P ( T | E ) = P ( E | T ) P ( T ) / P ( E ) .
min T J 1 ( T ) ,
J 1 ( T ) = Ω ( R T E log ( R T ) ) d x d y .
R ( x , y ) Ω R d x d y E R T = 1.
T k + 1 = T k × ( R ( x , y ) Ω R d x d y E R T ) .
E ( f ) = E ( p ) exp ( l 2 2 σ 2 ) ,
V = S x T ( x , y ) S x S y = 1 T ( x , y ) S y .
ε = δ t T S x S y = d S T S x S y V = a t a 2 2 T S x S y V = S x ( x T ) 2 2 a T 4 S y 2 ,
J 2 ( T ) = μ Ω | T | d x d y ,
min T ( J 1 + J 2 ) .
T k + 1 = T k 1 μ Δ T | T | × ( R ( x , y ) Ω R d x d y E R T ) .
E s = γ R T .
min γ | ( E E s ) η E f | ,
e l = | v x | S x S x S x ( x z ) 2 2 .
d = arccos v x · v y | v x | | v y | π 2 x z y z ,
v x = [ 1 , 0 , x z ] , v y = [ 0 , 1 , y z ] .
R ( θ ) = rot z ( R , θ ) ,
R ca ( ρ , θ ) = 1 360 0 360 R ( ρ , θ ) d θ .
E = R ca T .
ρ = k ( θ ) .
t ( ρ , θ ) = T ( ρ , θ ) ρ p ( θ ) d θ ,
p ( θ ) = 360 k ( θ ) .
v ( ρ , θ ) = ( d θ ) 2 + ( k ( θ ) d θ ) 2 t ( ρ , θ ) .
v ( ρ , θ ) 1 T ( ρ , θ ) ρ p ( θ ) .

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